Limits...
Neuronal firing sensitivity to morphologic and active membrane parameters.

Weaver CM, Wearne SL - PLoS Comput. Biol. (2007)

Bottom Line: We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain.Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function.Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Biomathematics, Mount Sinai School of Medicine, New York, New York, United States of America. christina.weaver@mssm.edu

ABSTRACT
Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

Show MeSH

Related in: MedlinePlus

Firing Rate Gain Sensitivity Across Constant Density and Constant Numbers Morphologic Spaces(A) Colormap representing baseline firing rate gain across CD morphologic space (colorscale 0–400 Hz/nA; top right); the gain of models firing irregularly at 300 or 600 pA was not calculated (gray cells). Black vertical line denotes models with the default value of D; arrow indicates that D was the main driver of baseline gain.(B) Gain sensitivity to RCa and 								 (top row) and to D + SA / CD and L + D / CD (bottom row). Models shown in gray fired irregularly. Arrows indicate the principal sensitivity direction with increasing D. Sensitivity to 								 was near zero throughout the space. Analogous colormaps across CN morphologic space are shown for (C) baseline firing rate gain and (D) gain sensitivity to parameter perturbations among candidate models. Arrows in (C) show that decreases in baseline gain followed D; the principal sensitivity directions in (D) follow this trend. Across constant number space, sensitivities to active parameters often had opposite sign for large versus small L values (“−” versus “+” in [D]). Among the candidate models, gain was more sensitive to D + SA than to all active parameters except 								 and sometimes 								.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g009: Firing Rate Gain Sensitivity Across Constant Density and Constant Numbers Morphologic Spaces(A) Colormap representing baseline firing rate gain across CD morphologic space (colorscale 0–400 Hz/nA; top right); the gain of models firing irregularly at 300 or 600 pA was not calculated (gray cells). Black vertical line denotes models with the default value of D; arrow indicates that D was the main driver of baseline gain.(B) Gain sensitivity to RCa and (top row) and to D + SA / CD and L + D / CD (bottom row). Models shown in gray fired irregularly. Arrows indicate the principal sensitivity direction with increasing D. Sensitivity to was near zero throughout the space. Analogous colormaps across CN morphologic space are shown for (C) baseline firing rate gain and (D) gain sensitivity to parameter perturbations among candidate models. Arrows in (C) show that decreases in baseline gain followed D; the principal sensitivity directions in (D) follow this trend. Across constant number space, sensitivities to active parameters often had opposite sign for large versus small L values (“−” versus “+” in [D]). Among the candidate models, gain was more sensitive to D + SA than to all active parameters except and sometimes .

Mentions: Most models across CD morphologic space fired regularly. A connected subset of these models fired doublets in response to 300–600 pA current injections (gray cells, Figure 9A). As with optimized models, such models were included in firing rate sensitivity analysis but were omitted for gain. Inspection of the relative timing of somatic and dendritic spiking revealed that the bursting mechanism lay within the soma of these models, and that dendritic membrane potential simply followed the somatic time course (unpublished data). While spontaneous firing rate largely followed SA, baseline gain exhibited a strong dependence on D (black vertical line, arrow) and minimal dependence on L, indicated by the vertical stripes of iso-gain values parallel to the L axis.


Neuronal firing sensitivity to morphologic and active membrane parameters.

Weaver CM, Wearne SL - PLoS Comput. Biol. (2007)

Firing Rate Gain Sensitivity Across Constant Density and Constant Numbers Morphologic Spaces(A) Colormap representing baseline firing rate gain across CD morphologic space (colorscale 0–400 Hz/nA; top right); the gain of models firing irregularly at 300 or 600 pA was not calculated (gray cells). Black vertical line denotes models with the default value of D; arrow indicates that D was the main driver of baseline gain.(B) Gain sensitivity to RCa and 								 (top row) and to D + SA / CD and L + D / CD (bottom row). Models shown in gray fired irregularly. Arrows indicate the principal sensitivity direction with increasing D. Sensitivity to 								 was near zero throughout the space. Analogous colormaps across CN morphologic space are shown for (C) baseline firing rate gain and (D) gain sensitivity to parameter perturbations among candidate models. Arrows in (C) show that decreases in baseline gain followed D; the principal sensitivity directions in (D) follow this trend. Across constant number space, sensitivities to active parameters often had opposite sign for large versus small L values (“−” versus “+” in [D]). Among the candidate models, gain was more sensitive to D + SA than to all active parameters except 								 and sometimes 								.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2211531&req=5

pcbi-0040011-g009: Firing Rate Gain Sensitivity Across Constant Density and Constant Numbers Morphologic Spaces(A) Colormap representing baseline firing rate gain across CD morphologic space (colorscale 0–400 Hz/nA; top right); the gain of models firing irregularly at 300 or 600 pA was not calculated (gray cells). Black vertical line denotes models with the default value of D; arrow indicates that D was the main driver of baseline gain.(B) Gain sensitivity to RCa and (top row) and to D + SA / CD and L + D / CD (bottom row). Models shown in gray fired irregularly. Arrows indicate the principal sensitivity direction with increasing D. Sensitivity to was near zero throughout the space. Analogous colormaps across CN morphologic space are shown for (C) baseline firing rate gain and (D) gain sensitivity to parameter perturbations among candidate models. Arrows in (C) show that decreases in baseline gain followed D; the principal sensitivity directions in (D) follow this trend. Across constant number space, sensitivities to active parameters often had opposite sign for large versus small L values (“−” versus “+” in [D]). Among the candidate models, gain was more sensitive to D + SA than to all active parameters except and sometimes .
Mentions: Most models across CD morphologic space fired regularly. A connected subset of these models fired doublets in response to 300–600 pA current injections (gray cells, Figure 9A). As with optimized models, such models were included in firing rate sensitivity analysis but were omitted for gain. Inspection of the relative timing of somatic and dendritic spiking revealed that the bursting mechanism lay within the soma of these models, and that dendritic membrane potential simply followed the somatic time course (unpublished data). While spontaneous firing rate largely followed SA, baseline gain exhibited a strong dependence on D (black vertical line, arrow) and minimal dependence on L, indicated by the vertical stripes of iso-gain values parallel to the L axis.

Bottom Line: We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain.Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function.Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Biomathematics, Mount Sinai School of Medicine, New York, New York, United States of America. christina.weaver@mssm.edu

ABSTRACT
Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

Show MeSH
Related in: MedlinePlus